DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

Article in volume

Authors:

Dr. Kumduang

Thodsaporn Kumduang

Department of Mathematics, Faculty of Science and Technology
Rajamangala University of Technology Rattanakosin
Nakhon Pathom 73170, Thailand

email: kumduang01@gmail.com

R. Chinram

Ronnason Chinram

Division of Computational Science
Faculty of Science, Prince of Songkla University
Hat Yai, Songkhla 90110, Thailand

email: ronnason.c@psu.ac.th

Title:

Fuzzy ideals and fuzzy congruences on menger algebras with their homomorphism properties

PDF

Source:

Discussiones Mathematicae - General Algebra and Applications 43(2) (2023) 189-206

Received: 2020-12-16 , Revised: 2021-11-28 , Accepted: 2021-11-28 , Available online: 2023-01-11 , https://doi.org/10.7151/dmgaa.1418

Abstract:

It is well known that Menger algebras, sometime called superassociative algebras, play a major role in both mathematical sciences and related areas. The notion of fuzzy sets was initiated by L.A. Zadeh as a general mathematical machinery of classical sets. The present paper establishes a strong interaction between fuzzy sets and Menger algebras. We show that the set of all fuzzy subsets on $G$ together with one $(n+1)$-ary operations forms a Menger algebra. The concept of several kinds of fuzzy ideals in Menger algebras is introduced and some related properties are investigated. Furthermore, we provide a construction of quotient Menger algebras via fuzzy congruence relations. Finally, homomorphism theorems in terms of fuzzy congruences are studied. Our results can be considered as a generalization in the study of semigroup theory too.

Keywords:

Menger algebra, fuzzy ideal, fuzzy congruence relation, quotient Menger algebra

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